Why not use a method of smothering and blocking out sunlight by creating a thick mulch of wood chips, leaves, etc? Anywhere from 6 inches to 12 inches will do this.
I have a bocking 14 variant so it may be different, but 6-8 inches of wood chips did nothing but slow my comfrey down and protect it from a late frost we had after our annual false spring. The leaves didn't even look weak or sickly whatsoever when they popped through! Maybe 12 inches would suffice, but I don't put anything past comfrey.
The one time I had to kill a flourishing plant, I waited until it started to wake up in spring soaked the area and put a 3 inch layer of whole, compacted damp leaves from last fall down with the intent of creating a wet enough environment to get some root rot going. I then topped the leaves with two pieces of cardboard all held down and buried in 6 inches or so of wood chips. That was two years ago and, so far, no comfrey, but I keep at least 6 inches of woodchips on top.
As so your original question about solarization, I have never done that, but I know of no reason why it wouldn't work in time. My only concern is in line with Anne's; you'll have to kill just about everything and everyone to ensure that the comfrey is also dead and gone.
Good luck obliterating one of my favorite plants!